The Bugatti Veyron occupies a unique spot among dealer showroom trophy cars: the fastest production automobile in the world. With a top speed of 254 miles per hour (406 kilometers per hour), the Veyron sits atop the supercar heap, chewing up asphalt at a brisk pace just under 4.3 miles per minute (over 6.7 kilometers per minute). If a Veyron graced my humble two-car garage, I could theoretically travel the 450 miles between my home office and Mentor Graphics’ company headquarters in Wilsonville, Oregon in less than two hours. Not a bad commute, but the road would have to be straight and flat to take advantage of the Veyron’s pavement burning speed. Even more impressive than the Veyron’s top speed performance, however, is the physics that govern it.
Physics was among my favorite subjects in both high school and college. For me it was the perfect marriage of mathematical theory with practical application. In short, physics was a reason to know math. While my skills in the nuts and bolts of physics have faded a bit over the years, I still have a great appreciation for the mathematics of how things work. With the Veyron in mind, I recently sat down with a colleague (whose memory for physics details is much better than mine) to discuss the mathematics of force and power that govern how a car moves down the road.
As it turns out, the faster a car moves, the more Mother Nature tries to hold it back. Assuming constant air density, coefficient of drag, and cross-section area, Mother Nature pushes back with a force proportional to the square of the car’s velocity. And to overcome this force, the car’s engine must deliver power proportional to the cube of that same velocity. It’s easy to see that, at high-speeds, these force and power versus velocity relationships produce some pretty amazing numbers.
I first stumbled across the Veyron while watching an episode of Top Gear (for brief Top Gear details, see my Top Gear = Driving Fun post). Among other fun facts about the car, James May of the Top Gear crew mentioned that the Veyron’s 16 cylinder engine produces an amazing 1000 horsepower. He then went on to explain that the Veyron can reach 155 MPH (248 KPH) using just 270 HP (201 kW). The remaining 730 HP is reserved to push the Veyron the remaining 99 MPH to its top speed. If you’re keeping track, that’s 27% of available horsepower to reach 61% of top speed. Covering the remaining 49% of rated top speed requires the remaining 73% of available horsepower. So to review: 270 HP required for 155 MPH; 730 HP required for the remaining 99 MPH. Veyron physics are both interesting and remarkable.
Analyzing the complex physics of vehicle operation, including Mother Nature’s strict and unforgiving rules that can hobble performance, is no small design feat, whether the vehicle is a Veyron-class super car, or a basic economy-class grocery getter. Automobiles represent some of the most complex, multi-physics design challenges for systems engineers. Efficiently integrating vehicle systems has pushed design techniques beyond traditional design-then-prototype development flows into the realm of virtual prototyping using computer-based development environments and techniques. SystemVision is one of a handful of multi-physics system modeling and analysis environments that can handle the complexities of multi-physics system modeling and analysis, and the only tool of its kind that is 100% standard language based (think VHDL-AMS, IEEE’s Std 1076.1).
To learn more about SystemVision’s standards-based modeling and analysis capabilities, click here. And if you want to see if a Veyron might suit that empty bay in your garage, and you happen to have an extra $1.7 million (base price) idling away in your checking account, click here.